Wikipedia: Bicycle and Motorcycle Dynamics
Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics is a branch of classical mechanics, which in turn is a branch of physics. Bicycles and motorcycles are both single-track vehicles and so their motions have many fundamental attributes in common.
Bike motions of interest include balancing, steering, braking, suspension activation, and vibration. Experimentation and mathematical analysis have shown that a bike stays upright when it is steered to keep its center of mass over its wheels. This steering is usually supplied by a rider, or in certain circumstances, by the bike itself. Long-standing hypotheses and claims that gyroscopic effect is the main stabilizing force have been discredited.
While remaining upright may be the primary goal of beginning riders, a bike must lean in order to maintain balance in a turn: the higher the speed or smaller the turn radius, the more lean is required.
(Shawn's Comment: This article is very geeky and technical but might be of some use in figuring out what happens when you ride.)
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Countersteering
This stuff can get deep real fast. Another interesting topic in Wikipedia is the section on countersteering, and if you really want to get confused look into the discussion part where the posters discuss things amongst themselves. I'm almost embarrassed to say I read this stuff but I can't help it, I find the science behind motorcycles fascinating.
I'm trying to learn more
I'm trying to learn more about the dynamics of the bike and how what I do on top affects how it rides and handles. If it doesn't get too geeky, I find it *very* informative and love going out to practice what I've learned!
Shawn King
Host, Your Bike Life